LTSS BTWN E120 AND FK10 WHILE ON VECTORS FOR PARALLEL APCHS. THE E120 WAS AT 9000 FT; THE FK10 WAS DSNDING TO 9000 FT. THE RPTR THOUGHT THE E120 HAD BEEN GIVEN DSCNT CLRNC TO 8000 FT. OPERROR. TCASII EVASIVE ACTION TAKEN BY BOTH ACFT. NMAC.

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WHILE ON A 160 DEG HDG TO JOIN FINAL RWY 16R; FINAL CTLR CLRED AN FK10 FOR A VISUAL APCH TO RWY 16L. THEY WERE NOT IN SIGHT AND WE WERE NOT YET NOTIFIED OF THEM BEING A POSSIBLE FACTOR. THEY WERE ABEAM THE SLC VOR IN R TFC. AS THEY BEGAN A R TURN (BASE LEG) FINAL CTLR CALLED THEM OUT AND WE IDENTED THEM. THEY WERE DSNDING THROUGH 9500 FT ON TCASII. AS WE RECEIVED A TA; ATC ADVISED US TO TURN R TO 180 DEGS; AND PASS BEHIND THE FK10. THAT WAS A VECTOR FOR A COLLISION AND I DID NOT EVEN HAVE TIME TO INITIATE IT. I SAW ON TCASII THE FK10 WAS STILL DSNDING SO I ADDED PWR AND CLBED AND TURNED TO A HDG OF 140 DEGS LEVELING OFF AT 10000 FT. MY FO SAID THE FK10 PASSED RIGHT UNDERNEATH OUR ACFT BY 200-300 FT. THE FK10 CAPT SAID HE ESTIMATED THE VERT SEPARATION AT 200 FT. HE ALSO SAID HIS TCASII GAVE HIM A CONFLICT RESOLUTION OF A CLB INSTEAD OF WHAT HE DID. HE SAID HAD HE BEEN IMC HE WOULD HAVE FOLLOWED IT AND IN HIS OPINION WE WOULD HAVE COLLIDED. WHEN WE WERE GIVEN THE 180 DEG HDG MY FO TOLD ATC THAT WOULD NOT WORK AND WE WERE ON A INTERSECTING COURSE WITH THE FK10; THE CTLR SAID 'DO WHATEVER YOU HAVE TO DO TO MISS THEM.' THAT WAS THE LAST WE HEARD FROM HER; SHE WAS VERY BUSY AND FORGOT EVEN TO HAND US OVER TO TWR. CONTINUED APCH TO AN UNEVENTFUL LNDG. CALLED SUPVR AT TRACON AND HE WAS CONCERNED; POLITE AND HELPFUL. HE SAID HE WOULD LOOK INTO IT TO CALL BACK FOR FOLLOW UP. WILL DO IT. HOW DID THIS HAPPEN? IN MY OBSERVATION; CTLR IN TRAINING AT RUSH HR; REACHED SATURATION. CTLR NOT AWARE OF POSSIBLE CONFLICT. CTLR GAVE VECTOR WHEN IT WAS TOO LATE TO TURN OUT OF THE WAY. CTLR CLRED FK10 TO DSND THROUGH OUR ALT AND LATERAL SEPARATION (INCURSION) BEFORE WE WERE MADE AWARE OF THEM. INADEQUATE SUPERVISION OF FINAL CTLR. SUPPLEMENTAL INFO FROM ACN 345680: WE RECEIVED TCASII TA WARNING HALFWAY THROUGH TURN; THEN A TCASII RA WARNING FOLLOWED IMMEDIATELY BY TCASII CLB COMMAND. I (CAPT) WAS FLYING; KICKED OFF THE AUTOPLT AND AUTOTHROTTLES AND STARTED A CLB. FOLLOWING THE CLB COMMAND PLACED US IN A DANGEROUSLY COMPROMISING POS; SO DSNDING L TURN WAS INITIATED. APPROXIMATE DISTANCE FROM OTHER ACFT ESTIMATED AT LESS THAN 500 FT VERT SEPARATION AND 500 FT LATERAL SEPARATION. SUPPLEMENTAL INFO FROM ACN 345660: I HAD THE FK10 ON DOWNWIND HDG 350 DEGS; DSNDING TO 9000 FT. THE E120 WAS BEING HANDED OFF NW OF SLC VOR. I THOUGHT I DSNDED THE E120 TO 8000 FT AND TOLD HIM TO EXPEDITE THROUGH 9000 FT.